Magneto-elastic combined multidimensional resonance of a rotating circular plate in a double-direction magnetic field
Zhe Li 1,2
Yu Da Hu 1,2
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School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao
Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao
Submission date: 2019-01-16
Acceptance date: 2019-05-06
Online publication date: 2019-10-15
Publication date: 2019-10-15
Journal of Theoretical and Applied Mechanics 2019;57(4):883-895
Magneto-elastic nonlinear non-axisymmetric resonance is investigated for a rotating annular plate in a double-direction magnetic field. According to transverse and longitudinal magnetoelastic non-axisymmetric vibration equations of the thin annular plate, and considering the influence of the static load term, non-axisymmetric vibration differential equations by combined parametric and forced excitations are obtained through application of the Galerkin method. Then, the method of multiple scales is applied to solve differential vibration equations. By numerical computations, the influence of magnetic induction intensity, inner and outer diameters, excitation and radial forces on transverse and longitudinal resonance characteristics are analyzed.
Awrejcewicz J., Krysko V.A., Krysko A.V., 2004, Complex parametric vibrations of flexible rectangular plates, Meccanica, 39, 3, 221-244.
Awrejcewicz J., Krysko V.A., Moldenkova T., 2006, Mathematical model of dissipative parametric vibrations of flexible plates with nonhomogeneous boundary conditions, Mathematical Problems in Engineering, DOI: 10.1155/MPE/2006/85623
Chen Y.R., Chen L.W., 2007, Vibration and stability of rotating polar orthotropic sandwich annular plates with a viscoelastic core layer, Composite Structures, 78, 1, 45-57.
Chonan S. Mikami T. Ishikawa H., 1986, The vibrations and critical speeds of rotating sawblades, The Japan Society of Mechanical Engineers, 52, 478, 1805-1812.
Hu Y.D., Li Z., 2017, Electromagnetic elastic coupling vibration equations of a conductive rotating circular plate, Chinese Journal of Applied Mechanics, 34, 1, 38-42.
Hu Y.D., Li W.Q., 2018, Study on primary resonance and bifurcation of a conductive circular plate rotating in air-magnetic fields, Nonlinear Dynamic, 93, 2, 671-687.
Hu Y.D., Li Z., Du G.J. Wang Y.N., 2018a, Magneto-elastic combination resonance of rotating circular plate with varying speed under alternating load, International Journal of Structural Stability and Dynamics, 18, 3, 1850032.
Hu Y.D., Rong Y.T., Li J., 2018b, Primary parametric resonance of an axially accelerating beam subjected to static loads, Journal of Theoretical and Applied Mechanics, 56, 3, 815-828.
Hu Y.D., Wang T., 2016, Nonlinear free vibration of a rotating circular plate under the static load in magnetic field, Nonlinear Dynamics, 85, 3, 1825-1835.
Hu Y.D., Zhang J.Z., 2013, Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field, Applied Mathematics and Mechanics, English Edition, 34, 11, 1405-1420.
Kang J.H., 2017, Axisymmetric vibration of rotating annular plate with variable thickness subjected to tensile centrifugal body force, International Journal of Structural Stability and Dynamics, 17, 9, 1750101.
Li Z., Hu Y.D., Li J., 2017, Magnetoelastic principal parametric resonance of a rotating electroconductive circular plate, Shock and Vibration, DOI: 10.1155/2017/5196847.
Ma N.J., Wang R.H., Han Q., 2014, Primary parametric resonance-primary resonance response of stiffened plates with moving boundary conditions, Nonlinear Dynamics, 79, 3, 2207-2223.
Maretic R., Glavardanov V., Radomirovic D., 2007, Asymmetric vibrations and stability of a rotating annular plate loaded by a torque, Meccanica, 42, 6, 537-546.
Narain S., Srivastava H.K., 2004,Magnetoelastic torsional vibration of non-homogeneous aeolotropic cylindrical shell of viscoelastic solids, Defence Science Journal, 54, 4, 443-454.
Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, John Wiley & Sons, New York.
Niu W.J., Zhang N.M., Yan X.P., Yang G.T., 2012, Nonlinear vibration of rectangular plate under the parametric excitation, Journal of Vibroengineering, 14, 3, 1076-1084.
Tylikowski A., Frischmuth K., 2003, Stability and stabilization of circular plate parametric vibrations, International Journal of Solids and Structures, 40, 19, 5187-5196.
Wu Q., Takahashi K., Chen B., 2007, Influence of cable loosening on nonlinear parametric vibrations of inclined cables, Structural Engineering and Mechanics, 25, 2, 219-237.
Xia Y., Wu Q., Xu Y., Fujino Y., Zhou X.Q., 2011, Verification of a cable element for cable parametric vibration of one-cable-beam system subject to harmonic excitation and random excitation, Advances in Structural Engineering, 14, 3, 589-595.
Yeh J.Y., 2011, Free vibration analysis of rotating polar orthotropic annular plate with ER damping treatment, Composites, Part B – Engineering, 42, 4, 781-788.
Younesian D., Aleghafourian M.H., Esmailzadeh E., 2015, Vibration analysis of circular annular plates subjected to peripheral rotating transverse loads, Journal of Vibration and Control, 21, 7, 1443-1455.
Zhang W., Huo Q.Z., 1991, Bifurcations of nonlinear oscillation system under combined parametric and forcing excitation, Acta Mechanica Sinica, 23, 4, 464-474.
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